Question: Solve for $x$ and $y$ using elimination. ${x+2y = 19}$ ${x-3y = -26}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-x-2y = -19}$ $x-3y = -26$ Add the top and bottom equations together. $-5y = -45$ $\dfrac{-5y}{{-5}} = \dfrac{-45}{{-5}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {x+2y = 19}\thinspace$ to find $x$ ${x + 2}{(9)}{= 19}$ $x+18 = 19$ $x+18{-18} = 19{-18}$ ${x = 1}$ You can also plug ${y = 9}$ into $\thinspace {x-3y = -26}\thinspace$ and get the same answer for $x$ : ${x - 3}{(9)}{= -26}$ ${x = 1}$